Year: 2026
Type: preprint
Abstract: We develop a new tree-search framework for mixed-integer linear programming problems, which incorporates a filter mechanism as a node-acceptance device. The introduced branch-and-filter algorithm combines proper branching actions with a filter on integrality violation and an incumbent-dependent objective coordinate. Inspired by classical filter methods in nonconvex constrained optimization, the proposed method moves to a restoration phase whenever sufficient progress cannot be provided by the filter and funnel mechanisms, the latter of which is anchored at global relaxation lower bounds. Under mild assumptions, the introduced method either certifies infeasibility in finitely many iterations, or converges to global optimality. Moreover, we establish a total outer iteration complexity bound of order $\mathcal{O}(\varepsilon^{-1})$ to certification of an $\varepsilon$-optimal mixed-integer solution through fixed-integer linear programming recovery. We finally perform several numerical experiments to study the performance of branch-and-filter against benchmark solvers, under a branch-and-bound, a branch-and-cut, and a novel cell-deletion realization of the proposed restoration oracle.
Source: arXiv (Cornell University)
Author: Dimou, Nikos
Institution: University of North Carolina at Chapel Hill
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223676098